Stimulated Brillouin scattering is a fundamental interaction between light and travelling acoustic waves and arises primarily from electrostriction and photoelastic effects, with an interaction strength several orders of magnitude greater than that of other relevant non-linear optical processes. Here we report an experimental demonstration of Brillouin-scattering-induced transparency in a high-quality whispering-gallery-mode optical microresonantor. The triply resonant Stimulated Brillouin scattering process underlying the Brillouin-scattering-induced transparency greatly enhances the light-acoustic interaction, enabling the storage of light as a coherent, circulating acoustic wave with a lifetime up to 10 μs. Furthermore, because of the phase-matching requirement, a circulating acoustic wave can only couple to light with a given propagation direction, leading to non-reciprocal light storage and retrieval. These unique features establish a new avenue towards integrated all-optical switching with low-power consumption, optical isolators and circulators.